Solve sqrt{100/6.28}

$$\sqrt{ \frac{ 100 }{ 6.28 } }$$

Evaluate

$$\frac{50\sqrt{157}}{157}\approx 3.990434422$$

Solution Steps

Expand \frac{100}{6.28} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{10000}{628}}$$

Reduce the fraction \frac{10000}{628} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{2500}{157}}$$

Rewrite the square root of the division \sqrt{\frac{2500}{157}} as the division of square roots \frac{\sqrt{2500}}{\sqrt{157}}.

$$\frac{\sqrt{2500}}{\sqrt{157}}$$

Calculate the square root of 2500 and get 50.

$$\frac{50}{\sqrt{157}}$$

Rationalize the denominator of \frac{50}{\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{50\sqrt{157}}{\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{50\sqrt{157}}{157}$$